The Mordell-Weil theorem states that the set of rational points on an abelian variety over a number field forms a finitely generated abelian group, hence isomorphic to a group of the form $T \oplus \Z^r$, where $T$ is a finite torsion group. The integer $r\ge 0$ is the Mordell-Weil rank of the abelian variety.
- Review status: reviewed
- Last edited by John Cremona on 2018-05-24 16:47:17
- 2018-05-24 16:47:17 by John Cremona (Reviewed)